1. Field of the Invention
This invention relates to apparatus for optical phase conjugation, and in particular to phase conjugation with spatially resolvable thresholding, which has applications to optical associative memories.
2. Description of Related Art
Phase conjugation is an optical phenomenon that has attracted considerable attention in recent years. Several different ways of producing phase conjugated beams have been discussed in the literature, including four-wave mixing, stimulated Brillouin scattering, three-wave mixing, and photon echo devices. A review of various applications of optical phase conjugation is presented by Giuliano in PHYSICS TODAY, April 1981, pages 27-35, "Applications of Optical Phase Conjugation". A general review of the field is given in the following references: A. Yariv, IEEE, J. Quantum Electronics QE-14, 650 (1978); D. M. Pepper, Optical Engineering 21, page 176, (1982); "Nonlinear Optical Phase Conjugation" by D. M. Pepper in The Laser Handbook, volume 4, edited by M. Bass and M. L. Stitch and published by North-Holland in New York in 1985; and the book Optical Phase Conjugation edited by R. A. Fisher, published by Academic Press in New York in 1983.
Basically, a phase conjugate reflector produces a retroreflection of an incident beam, with the phase of the reflected beam reversed at each point of reflection from that of the incident beam. Phase conjugate reflection plays a key role in the optical implementation of a type of memory system known as an associative memory.
An associative memory, in which information patterns are stored in such a way that introduction of one pattern or part of one pattern results in the recall of the complete stored pattern (homo-association) or of another (hetero-association), has potential applications in logical operations, pattern recognition, and image understanding. Various types of associative memories have been implemented and reported in the literature.
One approach to implementing such memories employs various algorithms for associative recall using matrix algebraic manipulations on a digital computer. A memory model based on matrix algebra has been described by J. J. Hopfield in his paper "Neural Networks and Physical Systems with Emergent Collective Computational Abilities," Proc. Natl. Academy of Science U.S.A., 1982, Vol. 79, pp. 2554-2558. The Hopfield model utilizes feedback and non-linear thresholding to force the output pattern to be the stored pattern which most closely matches the input pattern. A major drawback of this model is the large storage and computational effort required for manipulation of an association matrix used in the model. For the case of storing two-dimensional image patterns, a four-dimensional matrix is required.
Another approach to implementing an associative memory employs holograms, which are optical memories that are inherently associative in that input reference beams are used to recall associated images. It is a well known property of a hologram that when it is illuminated with a reference beam (referred to here as a probe reference beam) which corresponds to a stored-image-associated reference beam, it will produce an image (referred to here as a probe image) corresponding to the particular stored image with which that probe reference is associated. In a reciprocal manner, when the hologram is illuminated with a probe image corresponding to one of the stored images, the hologram will produce a probe reference beam which is the unique reference beam associated with that particular stored image.
It has also been found that when a probe image containing only a portion of a stored image is used to illuminate a hologram, the resultant probe reference beam generated consists of a composite of reference beams, primarily containing the correct stored-image-associated reference beam. Conversely, when a composite probe reference beam containing only a portion of a storedimage-associated reference beam is used to illuminate a hologram, the resultant probe image generated consists of a composite of stored images, primarily containing the correct stored image associated with that reference beam.
Besides the hologram, the phase conjugate mirror is another useful device for implementing an all-optical associative memory. In the early 1970s a new field emerged in the area of coherent optics, known as nonlinear optical phase conjugation (NOPC). As a result of studies and experiments in that field, the remarkable devices known as phase conjugate mirrors (PCMs) were developed. A rather complete discussion of PCMs, as well as a fairly exhaustive list of references in the field of NOPC, may be found in a paper by the inventor of the present invention, David M. Pepper, entitled "Nonlinear Optical Phase Conjugation," in Optical Engineering, Vol. 21, No. 2, March/April, 1982.
Briefly, a PCM is a device capable of producing a wavefront-reversed replica of a light beam incident on the mirror. This retroreflected beam, called a phase-conjugate beam, exactly retraces the path of the incident beam, ultimately returning to the point of origin of that beam. As an example of the properties of a PCM, consider a diverging beam of light coming from a point source in space. This spreading light wave will, after reflection from a PCM, become a converging beam of light which propagates back to exactly the same original point in space. This beam retracing occurs regardless of the angle of incidence of the beam with respect to the PCM. An ordinary plane mirror, on the other hand, changes only the direction of propagation of the incident optical beam. Thus, an incident diverging beam will continue to diverge after reflection from the mirror. Moreover, since the angle of reflection equals the angle of incidence for a flat mirror, tilting a flat mirror with respect to the angle of incidence results in a change in the angle of reflection which is twice the angle of tilt. A well-known use of a PCM is to restore the optical fidelity of an incident wave which has been distorted as it propagates from its source to the PCM, in consequence of the properties described above.
There are two major classes of PCM devices. One class employs the phenomenon of elastic photon scattering in an optically nonlinear medium. The medium may be chosen from a wide variety of gases (e.g. sodium vapor, carbon dioxide), solids (e.g. gallium arsenide, silicon, germanium) or liquids (e.g. chlorophyll, organics) as well as plasmas, liquid crystals, and aerosols. A particular type of PCM employing elastic photon scattering involves the interaction of four optical beams in the nonlinear medium. This type of PCM is known as a four-wave-mixing (FWM) PCM. The four beams involved include the incident input beam, the outgoing conjugate beam, and two input pump waves which act to sensitize the medium. One advantage of a FWM PCM is that it can be set up to amplify the phase conjugate beam to give it an amplitude exceeding that of the incident input beam.
Another class of PCM devices employs the phenomenon of inelastic photon scattering in a nonlinear medium. Interactions such as Raman, Brillouin, photorefractive, and Rayleigh scattering fall in this category. A feature of this class of PCMs is the passive nature of the phenomenon. The only optical beam required is the input wave to be conjugated. No additional sources such as pump waves are required. However, the amplitude of the conjugate wave is less than that of the input wave.
There is an excitation threshold associated with any self-pumped phase conjugate mirror, namely one involving a single input beam. With the other, nonthresholding types of phase conjugators it is possible, by putting sufficient power into the pump beams, to make an "amplifying" PCM with a reflectivity greater than unity. All these phenomena are described in articles and books covering the topic of nonlinear optics, such as, for example, the third edition of the book entitled Optical Electronics, written by Amnon Yariv and published in 1986 by Holt, Rinehart, and Winston in New York; the article "Nonlinear Optical Phase Conjugation" by D. M. Pepper in The Laser Handbook, volume 4, edited by M. Bass and M. L. Stitch and published by North-Holland in New York in 1985; and the book Optical Phase Conjugation edited by R. A. Fisher, published by Academic Press in New York in 1983.
An associative holographic memory apparatus employing phase conjugate mirrors is disclosed in the U.S. Pat. application entitled "Associative Holographic Memory Apparatus Employing Phase Conjugate Mirrors," by Marom et al., Ser. No. 786,884, U.S. Pat. No. 4,739,496, and in a continuation-in-part of that application entitled "Associative Holographic Memory Apparatus Employing Phase Conjugate Mirrors and a Two-Wave Mixing Contra-Directional Coherent Image Amplifier," by Owechko et al., Ser. No. 821,237, both assigned to the assignee of the present invention, Hughes Aircraft Company. These applications disclose apparatus for recalling a stored image by using an input image which includes a portion of the stored image. The apparatus includes a hologram having the stored image written on it simultaneously with a stored-image-associated reference beam. The hologram has the properties of providing a probe reference beam in response to an incident probe image and, in a reciprocal manner, of providing the probe image in response to the probe reference beam.
Two phase conjugate mirrors are employed in the basic configuration. The first phase conjugate mirror includes a thresholding function whereby a phase conjugate of only those components of the probe reference beam which exceed a predetermined threshold level of beam intensity is conveyed back to the hologram. The threshold can be either "hard" or "soft" (i.e., there can be either a strong or weak dependence to the phase conjugate reflectivity as a function of incident intensity). The first phase conjugate mirror may also include amplification so that the amplitude of the phase conjugated probe reference beam can be greater than that of the probe reference beam. The level of amplification can be made sufficient to overcome any undesirable losses in the hologram and the second phase conjugate mirror, whereby a phase conjugate resonator cavity is formed by the combination of the first and second mirrors. The resonator cavity acts to cause the output image to converge to the stored image. Alternate embodiments of the invention are described which employ a multiple storage and erasure hologram, and which employ only a single phase conjugate mirror.
Using a phase conjugate mirror to provide the thresholding function limits the choice of phase conjugate mirrors to the class of "self-pumped" phase conjugation devices. However, once a given beam is above the threshold of this class of phase conjugate mirrors, any beams that spatially overlap the region in the mirror that contains the first beam will also be reflected (conjugated), thereby negating the desirable thresholding type of discrimination sought. For the implementation of an efficient all-optical associative memory it would be highly desirable to use a spatially resolving phase conjugate mirror with a threshhold characteristic. No such device exists in the related art. It has been postulated that an array of independent phase conjugators, each with its own threshold characteristic, can fill this requirement. For example, an array of pumpless conjugators such as stimulated Brillouin cells or photorefractive media has been suggested. However, the phase relationships among an array of pumpless conjugators are randomly distributed because of the random noise distributions from which each conjugator is "seeded." Unless the conjugator array is capable of maintaining the same phase relationship of the spatial components of the incident and retroreflected beams, the system will not function efficiently, especially in the case of a heteroassociative memory configuration. The second phase-conjugate mirror (PCM) wavefront-reverses the object beam. The object beam contains a complex distribution of plane waves, whose relative phase must be preserved upon reflection in order for the system to function properly. In general, this PCM is not a thresholding type of device. However, in certain applications, it may be desirable to implement a spatially resolvable thresholding operation in addition to the conjugation function. In such a case, the relative phase relationship must be preserved.